As a stylus or another pen-tip moves through a two-dimensional or three-dimensional space, the pen-tip's location can be sampled, thereby providing data points indicating one or more curves through which a digital ink curve can be rendered. Depending on factors such as the speed of the pen-tip, the path followed by the pen-tip, and the sampling rate, the data points may be either more or less accurate in their approximation of the actual curve followed. Such accuracy may be the most important criterion for evaluating a curve which is visually rendered through or near the data points. The foregoing observations are made with the present claims in mind. Accordingly, one of skill in the art who did not have access to the claims would not necessarily have recognized the observations made here.